Unit 3 Potentiometry-II (Ph Metry)

Electroanalytical Methods -I

UNIT 3 POTENTIOMETRY-II (pH METRY) Structure 3.1

Introduction Objectives

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10

3.1

Concept of pH Glass Membrane Electrodes pH Meter Measurement of pH pH Titration Modified Glass and Solid State Membrane Electrodes Summary Terminal Questions Answers

INTRODUCTION

In the previous unit, you have seen that potentiometric methods mainly include two major types of analysis. First being direct measurement of an electrode potential from which the activity (or concentration) of an active ion may be derived. The other type involves, measuring the changes in the electromotive force (emf) brought about by the addition of a titrant to the sample. The principle of potentiometry can be applied to measure the emf, in terms of pH unit on pH scale by suitable modifying the common voltmeter to high input impedance mV meter. The acid-base titrations, involving measurement of change in pH to detect the end point, can be termed as pH metry instead of potentiometry. Objectives of developing pH metry lies in recognising the importance of pH, the very important test performed in studying chemical, biochemical, microbiological processes involved in various unit operations and processes in small to large scale industrial productions. In every phase of water and wastewater treatment processes, i.e. in acid-base neutralization, water softening, precipitation, coagulation in the field of both production and environmental protection technologies, all these processes are carried out at specific range.

Objectives After studying this unit, you should be able to: •

draw and level a glass electrode,

•

write the Nernst equation for a glass electrode,

•

describe how the pH meter can be used to measure the pH, and

•

describe how the pH data can be used to determine the equivalence point in acid base titrations, and

•

list the applications of ion-selective electrodes

3.2

CONCEPT OF pH

At a given temperature the intensity of the acidic or basic character of a solution is indicated by pH or hydrogen ion activity. By definition it is the negative logarithm of the hydrogen ion activity a + . H

56

pH = – log a

H

Potentiometry-II (pH Metry)

+

In dilute solution the hydrogen ion activity is approximately equal to the concentration of hydrogen ion. Pure water is very slightly ionized and at equilibrium the ionic product is [H+][(OH–] = Kw = – 1.0 × 10-14 at 25°C or [H+] = [OH– ] = 1.005 × 10-7 A logarithmic form is – log [H+] – log [OH– ] = –log Kw or pH + pOH = pKw From the above equilibrium it is clear that the pH scale for an aqueous solution lies between 0 and 14. The pH of most raw water sources lies within the range of 6.5-8.5, slightly basic due to the presence of bicarbonates and carbonates of the alkali and alkaline earth metals. The pH is generally measured with glass electrode and a pH meter. The glass membrane electrode or glass electrode is one of the most common examples of an ionselective indicator electrode. The overall cell, when the glass electrode is used with an external reference electrode such as standard calomel electrode (SCE), can be represented by: Glass membrane H +

SCE

To compute the cell potential, it could be assumed that the SCE is more positive than the glass electrode. Thus,

Ecell = ESCE + Ej – (E oG – 0.059 log[H+]) where Ej is liquid-junction potential and E oG is the standard electrode potential of the glass electrode. or Ecell = E* + 0.059 log [H+]

… (3.1)

Ecell = E* – 0.059 pH

… (3.2)

In terms of pH, Thus, cell potential is directly proportional to pH i.e. :

Ecell ∝ pH *

where E includes the standard electrode potential of glass electrode, potential of reference electrode and liquid-junction potentials between the reference electrode and solution. Beside these three potentials there is another potential called the asymmetry potential which is also contributing to this. Asymmetry potential is a small potential which exists across the membrane, even when the inner reference solution and the test solution are identical. The sources of asymmetric are not much clear. It may be due to the degree of hydration of the inner and outer surface of the glass membrane or due to its structural design or due to mechanical and chemical attack whilst in use. The degree of hydration of outer surface will also change if the electrode is allowed to dry out for some time. Because of this it is advised that the electrode should be stored either in water or in damp cotton wool. It is not possible to determine the value of asymmetry potential, therefore, it is necessary to calibrate glass membrane electrode with suitable buffer solutions. As the value of the asymmetry potential can change with electrode use, it is necessary to carry out calibration at least daily.

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Electroanalytical Methods -I

SAQ 1 Why is it necessary to calibrate the glass electrode before use? …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………...

3.3

GLASS MEMBRANE ELECTRODES

The pH glass electrode although somewhat mechanically fragile, resists a variety of sample media and with the exception of hydroxide is largely free from interferences. Moreover, pH-sensitive glass electrodes form the basis of many successful sensors for environmentally sensitive gases. Thus, glass membranes represent an important class of solid-membrane ion selective electrodes (ISEs). As illustrated in Fig. 3.1(a), these electrodes have thin glass membrane fused to the end of a glass or plastic body. The main body of the electrode contains an internal reference electrode typically Ag/AgCl and is filled with a solution that is usually the The majority of pH electrodes available commercially are combination electrodes that have both glass H+ ion sensitive electrode and additional reference electrode conveniently placed in one housing (see figure below). For some specific applications separate pH electrodes and reference electrodes are still used they allow higher precision needed sometimes for research purposes. In most cases combination electrodes are precise enough and much more convenient to use.

aqueous HCl of concentration around 1.0 mol dm −3 . The selectivity coefficient of glass-membrane is such that excellent dissemination against common cationic species is achieved.

(a)

(b)

Fig. 3.1: Glass electrode: (a) Typical glass electrode consisting of both an indicator glass electrode and a silver/silver chloride reference; (b) illustration showing an ion exchange

Combination electrodes

58

The pH electrode responds to hydrogen ions as a result of the thin ion-exchange sites on the surface of a hydrated glass membrane. The electrode consists of a thin layer of glass, typically about 50 µ m thick. Charge is transported across the membrane by sodium or lithium ions within the glass. The membranes are primarily made from Lithia (Lithium oxide) or sodium oxide, and SiO2, and some amount of Al2O3 and B2 O3 or multi-component glasses whose sensitivity pattern depends on the composition of the glass. The surface layer of the glass consist of silicate group associated with sodium ion (- Si O − Na + ) as shown in Fig. 3.1 (b). When this electrode is dipped in water, the sodium ions exchanged with the protons in water.

- Si O − Na + + H +

− SiO − H + +

→

Surface of solution Glass electrode before hydration

Potentiometry-II (pH Metry)

Na+

Glass surface after hydration

If glass electrode is placed in a test solution its glass membrane will have an inner and outer hydrated layers and potential difference is developed due to the difference in hydrogen ion activities between test solution and outer hydrated surface of glass electrode as well as inner solution and inner hydrated surface. This potential is called boundary potential and it varies with the activity or pH of the solution. Overall boundary potential is the potential difference between both the boundary potentials. We can write chemical equation for both the boundary potentials H + Gl − (s )
H + (aq) + Gl −

Outer surface of glass

Outer solution

H + Gl − (s )
H + (aq) + Gl −

Inner surface of glass

… (3.3)

… (3.4)

Inner solution

For the Eq. (3.3), the boundary potential is E1 ∝ (a1 – ah)

where a1 and ah are the activity of the hydrogen ions in the test solution and the outer hydrated layer, respectively. Similar for Eq. (3.4), the boundary potential is E2 ∝ (a2 – ah)

where the activity of inner solution is a2. Thus, overall boundary potential, Eb = E1 – E2 ∝ (a1 – ah) – (a2 – ah)

If we assume that the activities of the hydrogen ions in the inner and outer hydrated layer are the same, the above equation can be written as: Eb ∝

(a1 – a2)

But the activity of the hydrogen ions in the inner solution is a constant and this equation reduces to: Eb ∝ a1 Eb can be expressed for can in Nernst form: Eb = E1 – E2 = 0.0591 log

a1 a2

Eb = K1 + 0.0591 log a1 = K1 – 0.0591 pH

… (3.5)

where K1 is constant, it includes the constant factor related to hydrogen ion activity of inside solution, a2, that is, 0.0591 log a2. Thus, the boundary potential is a measurement of the hydrogen ion activity or the pH of the external solution. For measuring pH with glass electrode the arrangement shown in Fig. 3.2 are commonly employed. This arrangement has glass electrode with Ag/AgCl internal reference electrode and external reference electrode such as

59

Electroanalytical Methods -I

saturated calomel electrode (SCE). For such arrangement complete cell may be represented as: Reference electrode │ H+ │ Glass membrane │ H+ ║ Reference electrode (internal) (internal) (extenal) (SCE)

Glass electrode

Fig. 3.2: A typical electrode system for measuring pH

The cell potential is expressed as Ecell = (E ind ) – ESCE + Ej

… (3.6)

where ESCE is the potential due to external reference electrode, Ej is liquid-junction potential, and E ind is electrode potential of the glass electrode, which is actually a combination of three components: (i) the boundary potential, Eb, (ii) the potential of the internal Ag/AgCl reference electrode, and (iii) the asymmetry potential, Easy. From Eq. (3.5), substitute the value of Eb. Thus, Ecell = (Eb + EAg/AgCl + Easy) – ESCE + Ej

… (3.7)

Substitute the value of Eb in this equation Ecell = (K1 + 0.0591 log a1 + EAg/AgCl + Easy) – ESCE + Ej

or Ecell = E* + 0.0592 log a1 = E* – 0.0591 pH

… (3.8)

*

where E is a constant, it includes all the constants and near constant source of potentials, i.e. potential of both reference electrodes, liquid-junction potential between the external reference electrode and the solution, asymmetry potential and internal boundary potential. It is very difficult to determine the value of E* both experimentally as well as theoretically. Therefore, calibration method is used to eliminate this factor. In this method, first test solution is comprised of a standard buffer solution with the pH precisely known. Thus, for the standard, we can write following expression: (Ecell )s = E* – 0.0592 (pH)s

… (3.9)

This step is followed by measurement of cell potential for unknown solution. The expression will be (Ecell )u = E* – 0.0592 (pH)u

60

… (3.10)

Potentiometry-II (pH Metry)

To eliminate E* subtract Eq. (3.9) from Eq. (3.10), we find (pH)u = (pH)s –

( E cell ) u − ( E cell ) s 0.0591

… (3.11)

Eq. (3.11) has been adopted throughout the world as the operational definition of pH. pH determination using glass electrode is most accurate and widely used method despite a few disadvantages viz. the glass membrane being very fragile, it requires great care while using. The ordinary potentiometer cannot be used for measuring the potential of the glass electrode. Thus, the electronic potentiometers are required to be used, needs frequent standardization and, cannot be employed in pure ethyl alcohol, acetic acid and gelatin. The following features of glass electrode have made it more versatile to be used be as indicator electrode for pH measurement. •

It may be used in the presence of strong oxidizing and reducing solutions in viscous media and in presence of proteins which interfere with operation of other electrodes.

•

It can be used for solutions having pH values 2 to 10 with some special glass, measurements can be extended to pH values greater than 10.

•

It is simple to operate and immune to poisoning.

•

The equilibrium is reached quickly

While measuring pH you should be little care full as there are few factors which limit the accuracy of pH measurements. We are listing few of them below: 1.

The alkaline error: It is noticed that the ordinary glass electrode becomes sensitive to alkali ions and gives low reading in high pH range – above 9 or 10 pH units. The reason for the error is that whilst the glass membrane is selective to hydrogen ion, it also responds to other ions. This becomes more significant when the activity of the other ions is higher to activity of the hydrogen ion. Fig. 3.3 shows the error produced by different cations at different concentrations. You may have noticed that alkaline error is relatively more in case of sodium ion. This is because of higher selective coefficient of sodium ion. This due to sodium ion can be reduced by the use of Li2 O glass in place of Na2O glass.

Fig. 3.3: Deviation in pH measurement using a glass electrode under alkaline conditions

2.

The acid error: At low pH range – less than 0.5, the values determined by the glass electrode tend to be somewhat higher. This error is due to the activity of water which we have ignored while writing Nernst equation for the indicator electrode. We have assumed that activity of water may be taken to be unity as it is in large excess in the solution and it behaves as a pure substance. However, in highly acidic solution, the activity of the water becomes less than unity because a good amount is used in hydrating the protons. Similar effects are also observed

61

Electroanalytical Methods -I

on addition of large amount of any dissolved salt and on addition of a miscible non-aqueous solvent such as ethanol. The net result in each case is the measured pH will be too high. 3.

Variation in junction-potential: In most of the cases the composition of the standard buffer solution and test solution are different. In such situation, the liquid junction potential will be different.

4.

Error in the pH of the standard buffer: There may be possibility that buffer solution is not prepared with full care or its composition may change during storage. All these factors will cause an error in subsequent pH measurements.

5.

Temperature: A change in temperature may affect on pH measurements, because change in temperature affects the activities of the ions as well as the liquid-junction potentials. Therefore, it is advised to calibrate the electrode at the temperature of the test solution.

6.

Calibration procedures: Buffer solution cannot be prepared more accurately than ± 0.01 pH units. Therefore, we cannot calibrate the electrode better than this.

7.

Equipment related: These errors may due to the power fluctuations, parallax errors in reading analogue scales, etc.

With this theoretical background now we will see how the pH is measured using pH meter, but before that try following SAQs.

SAQ 2 How will you define boundary potential? …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... ...........................................................................................................................................

SAQ 3 List some factors which may cause errors in pH measurements. …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... ..........................................................................................................................................

3.4

pH METER

The instrumentation required to perform potentiometric measurements includes a reference electrode, an indicator electrode and a high input-impedance mV (pH/pion) meter as depicted in Fig 3.2. Ordinary laboratory volt meters cannot be used for the measurement of the emf of a glass electrode cells because of the high electrical resistance of glass electrode (typically 10-200 megaohms), special high-impedance voltmeter circuits are required, which draw 10-12 amperes or less from the circuit. The pH meter is a voltmeter but with several critical addition functions. Not only does it measure the potential across the pH-sensing and reference electrode system, but it also converts the potential

62

difference measurement at a given temperature into pH terms, and it provides mechanisms to correct for the non-ideal behaviour of the electrode system. The operational amplifier not only serves as high-impedance voltmeter, but also provides stability and automatic operation through the use of the feed-back loop. The operational controls on a pH meter are best understood by reference to the operational manual provided by manufacture of individual instrument. Modern electronic techniques permit the production of simplified pH meter that measures pH with an accuracy of + 0.1 pH unit. The microprocessor equipped pH meters include a temperature probe to display temperature compensation, a memory for the pH values of standard buffers, a waiting period to allow draft before taking pH readings and built in diagnostics to alert for electronic malfunctions or defective electrodes. Along with pH meter we also require a reference electrode and a glass membrane electrode which acts as indicator electrode in pH measurement. Details of reference electrode were discussed in earlier unit of this block and details of glass membrane electrode were discussed in previous section. •

Potentiometry-II (pH Metry)

The two most popular types of reference electrode are Reference Electrode: the saturated calomel and silver/silver chloride systems. Both types of reference electrodes exhibit many of ideal characteristics, those include maintaining fixed potential over time and temperature, having long-term stability and returning to the initial potential after being subject to small currents. i)

The saturated calomel electrode (SCE) is composed of metallic Hg, solid mercurous chloride (Hg2Cl2 ) and a saturated solution KCl a equilibrium. Consequently, the potential of the SCE (+0.241/2 V versus the standard hydrogen electrode) remains constant even if some of the liquid evaporates over time. The SCE is more popular and with a constant temperature bath, the error caused by fluctuating temperature can be eliminated. The SCE can be used as a reference electrode in a sample that does not exceed 80° C.

ii)

The Ag/AgCl electrode includes a silver wire, coated on one end with the insoluble AgCl salt. When the electrode is immersed in a saturated KCl solution, its potential at 25 ° C depends only on the Cl − concentration and is +0.192V versus the standard hydrogen electrode. The Ag/AgCl electrode should not be used in the solutions that contains species that can precipitate or complex with silver. Reference electrode should be prepared and maintained so that the level of the internal liquid is kept above sample solution to avoid infusion of sample into reference electrode. This is a commonly used precautionary measure to avoid any contamination of the sample by Cl − , Ag + or Hg 2+ ions.

•

3.5

Indicating Electrode (glass electrode): As described in Section 3.3.

MEASUREMENT OF pH

pH measurements are part of routine tests done to check and comtroll many our day to day activities like potable water quality, soil usability for different plants, water quality in aquaristics, they are done to control industrial processes, in wine-making and beer-making, to check milk quality, to check cosmetics - not to mention all labs throughout the world where pH measurements are performed many times a day to control reactions and analysis conditions. pH can be measured in several ways, of which two are widely used. One - simple and often enough precise - is a use of colorimetric indicator methods, i.e. use of pH strips

63

Electroanalytical Methods -I

(pH papers). Second, more costly and more demanding in terms of procedure that have to be used, but giving much more precise results - is a potentiometric method with usage of glass electrodes and pH meters. Colorimetric (spectroscopic) methods have never gained much popularity, although they are occasionally used in places where glass electrodes. The mail disadvatage of this procedure is that it can't be immersed in the test solution. Thus, the pH determination is usually done by potentiometric methods, which is the most accurate methods and free of interferences. Potentiometric Method of pH Measurement

The pH is determined by measurement of the emf of a cell comprising an indicator electrode (an electrode responsive to hydrogen ions such as glass electrode) immersed in the test solution and a reference electrode (usually a saturated calomel electrode, SCE) contact between the test solution and the reference electrode is achieved by means of liquid-junction, which form the part of a reference electrode. The emf of this cell is measured with pH. The description of pH-meter has already been made in Section 3.4, however procedure for stepwise calibration of pH meter and measurement of pH of a test sample is given below: Apparatus

a)

pH meter: consisting of potentiometer, a glass electrode, a reference electrode and a temperature compensating device. A balanced circuit is completed through potentiometer when the electrodes are immersed in the test solution.

b)

Reference electrode: consisting of a half-cell that provides a standard electrode potential. General colomel (SCE) or silver/ silver-chloride electrodes are used as a reference electrode.

c)

Glass membrane electrode: Several types of glass electrodes are available. Even combination (glass and reference) electrodes are available for pH measurement of different test solutions and at varying test conditions.

d)

Beakers: Preferably use polyethylene or TFE beakers.

e)

Stirrer: Use a magnetic TFE coated stirring bar.

Reagents Calibrate the electrode system against standard buffer solutions of known pH: Buffer tablets having pH 4.0, 7.0 and 9.2 are commercially available. Because buffer solutions may deteriorate as a result of mold growth or contamination, prepare fresh as needed. Alternatively buffer solutions can also be prepared as following: pH 4 buffer solution : Dissolve 10.2 gm anhydrous potassium biphthalate (KHC8H4) using boiled and cooled distilled water. Dilute to 1 dm3 . pH 7 buffer solution: Dissolve 1.361 gm anhydrous potassium dihydrogen phosphate (KH2 PO4), and 1.42 gm anhydrous disodium hydrogen phosphate, Na2HPO4 both of which have been dried at 110ºC to 130ºC. Use distilled water which have been boiled and cooled. Dilute to 1 dm3. pH 9.2 buffer solution : Dissolve: 3.81 gm borax (Na2B4 O7 10H2O) in distilled water. Dilute to 1 dm3. Procedure

Numerous pH meters of various designs are marketed by several instrument manufactures. General purpose pH meters are either line operated instruments that are

64

readable to 0.05 pH unit or battery operated instruments suitable for field job. These days digital pH meters readable to 0.01 pH unit are more popular as compared to scale-needle instruments.

Potentiometry-II (pH Metry)

Measurement of pH of a solution with the instrument (analog meter) shown in Fig. 3.4 can be made following the procedure given below in a step-wise manner. 1.

Keep the selector switch on ‘zero’ position and adjust the zero position by a screwdriver if the pointer does not indicate zero.

2.

Before using pH meter, remove electrodes from storage solutions (recommended by manufacturer) and rinse with distilled water. Dry electrodes by gently blotting with a soft tissue paper.

3.

Mount the electrodes in the clip on the stand.

4.

Connect the power cable to a 220V AC supply. Switch on the instrument and wait for a few minutes till the instrument warms up.

5.

Adjust the temperature/solution temperature value.

6.

Take the standard buffer solution of desired range (e.g. buffer of pH 4 for acidic solutions) in a beaker. The electrode assembly is immersed in the pH reference buffer and the solution is agitated gently by swirling the solution in the region of the glass electrode surface so as to bring it into pH equilibrium. It should be ascertained that the glass electrode membrane is completely immersed in the solution. The electrodes should not touch each other or the side or the bottom of the beaker. II

III

VII

IV

I

VI

V

Fig. 3.4: A direct reading pH meter (front view) legend: I. On/off switch II. Set zero III. Selector IV. Electrode support V. Temperature compensation VI. Set buffer VII. Meter

7.

Put the selector switch to suitable pH range (0-7 for acidic or 7-14 for basic solutions) and adjust set buffer knob in manner that the pointer reads the pH of the standard buffer solution (placed in the beaker).

8.

Put the selector switch back to zero position. Remove the electrodes from the buffer solution, wash the electrodes with distilled water and wipe them gently with tissue paper.

9.

Immerse the electrodes in a second buffer below pH 10, approximately 3 pH units different from the first one; the reading should be within 0.1 units for the pH of the second buffer. (If the meter response shows a difference greater than 0.1 pH unit from expected value looks for trouble with the electrodes or pH meter.

10.

Transfer the standard buffers back to the storage bottle and wash the beaker well with distilled water.

11.

Take the sample solution in the beaker. Introduce the electrodes in the solution and swirl it gently.

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Electroanalytical Methods -I

12.

Set the selector switch in the suitable range position and read the pH on the scale.

13.

Put the selector switch back to zero position. Remove the electrodes from the solution, wash them with distilled water and keep the electrodes in distilled water, when not in use.

Precautions

i)

Never touch the membrane of the glass electrode with anything else except soft tissue paper since it is fragile and is easily ruined if scratched or bumped.

ii)

The electrode(s) must not be removed from the solution unless the selector switch is at zero.

iii)

Never dip the glass electrode in a solution with a dehydrating action.

iv)

For sample analysis establish equilibrium between electrodes and sample by stirring sample to ensure homogeneity and measure pH.

v)

If used for measuring pH of albuminous substances, the glass electrode must be cleaned with suitable solvents and then the electrode is placed in distilled water for a few hours before it is used to measure the pH of the other solution.

vi)

For basic solutions with pH more than 11, glass electrodes of special composition are required to avoid interference due to sodium ion.

vii)

The glass electrode may be covered with a sleeve to save it from jerks.

viii) The standard buffer of pH value as close as possible to the sample pH value must be taken for the calibration of the system. Commercially available standard buffers of pH values 4, 7 and 9.2 are commonly used.

3.6

pH TITRATION

Similar to potentiometric titrations, in contrast to direct pH measurements, pH titrations generally offer increased accuracy and precision. Accuracy is increased because, measured pH are used to detect rapid changes in activity that occur at equivalence point of the titration. Furthermore, it is the change in pH versus titre volume rather than absolute value of pH that is of interest. Thus, the errors due to liquid-junction potentials and activity coefficients are minimized. pH titrations may be applied to a variety of systems including those involving weak acids and weak bases. In such titration, it is difficult to get end point using indicator method. A typical acidbase titration using pH metry is briefed as follows. It is known that the neutralization of acids and bases is always accompanied by the changes in the concentration of H+ and OH − ions. It is evident that hydrogen electrode may be employed in these titrations. The reference electrode used in these titrations is 1 M-calomel electrode. The apparatus used for acid-base titrations is as shown in Fig. 3.5. The critical problem in titration is the recognition of point at which the quantities of reacting species are presented in equivalent amounts, i.e. the equivalence point. The titration curve can be followed point by point plotting as the ordinate successive values of the pH versus the corresponding volume of titrant added as the abscissa. Addition of the titrant should be the smallest accurately measurable increments that provide an adequate density of points, particularly in the vicinity of equivalence point. •

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Over most of the titration range the pH varies gradually, but near the end point the pH changes very abruptly. The resulting titration curve resembles Fig. 3.6 (a).

Potentiometry-II (pH Metry)

Fig. 3.5: Typical Instrumental set up for pH titration

•

By inspection, the end point can be located from the inflection point of the titration curve.

•

This is the end point that corresponds to maximum rate of change of pH per unit volume of titrant added (0.05 cm3 or 0.1 cm3).

•

The distinction of the end point increases as the reaction involved becomes more nearly quantitative.

•

Once the pH has been established for a given titration, it can be used to indicate subsequent end points for the same chemical reaction.

•

The equivalence point can be more precisely located from the 1st and 2nd derivative curves as illustrated in Fig. 3.6 (b) and 3.6 (c). Solutions more dilute than 10-3 M generally do not give satisfactory end points. This is limitation of pH metry and potentiometric titrations.

(a)

(b)

(c)

Fig. 3.6: pH titration curves; (a) Normal curve; (b) First derivative curve; and (c) second derivative curve `

Titration of a Weak Acid with a Strong Base

So far titration curve shown in Fig. 3.6 (a) describe the progress of the titration of strong acid and strong base. We now consider the titration of 25 cm3 of 0.05 M CH3COOH solution with 0.05 M NaOH solution to explain how the pH of the titration is changed at different stages of the titration. For this purpose we will be using many expressions used in theory of neutralization titrations which you may have studied in first course on ‘Basics of Analytical Chemistry or in your undergraduate physical chemistry courses.

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Electroanalytical Methods -I

Starting point of the titration curve: The starting point of the titration curve of 0.05 M CH3COOH solution is considerably lower than that of 0.05 M HCl solution. This is because acetic acid is dissociated almost by 100 times less than hydrochloric acid. (the degree of electrolytic dissociation of 0.05 M CH3COOH solution α ≈ 1 per cent; for 0.05 M HCl solution, α ≈ 90 per cent). Hence [H+] in 0.05 M CH3 COOH solution is also 100 times less than in 0.05 M HCI solution. And pH will be 3, and not unity.

A more precise pH value of the starting point of the titration curve is found by the following way. Write the expression for acid dissociation constant for acetic acid: Hydrolysis of salt of a weak acid and a strong base may be represented as A − + H2O
HA + OH − Hydrolysis constant is given by [HA ] [OH − ] Kh = [A − ] [ HA ] [OH − ] [H + ] = [ A − ] [H + ] =

Kw

But at equilibrium, [HA] = [OH − ], therefore,

[OH − ] 2 [OH − ] = − c salt [A ] 2 Kw = .(ii) [ H + ] 2 c salt Combining Eqs. (i) and (ii) gives Kh =

2 Kw [H + ]2 c

= salt

Kw

At equilibrium, [H + ] = [ A − ] . As the degree of ionization of acetic acid is small,

therefore at equilibrium, the concentration of unionized acid is approximately equal to total concentration of acid(cacid), i.e. cacid = [HA] + [A − ] ≈ [ HA] . Therefore, 6

Ka =

[H + ]2 [H + ]2 = [ HA] cacid

[H+] =

K a c acid

For acetic acid K a = 1.75 × 10 −5 [H + ] = 1.75 × 10 −5 × 0.05 M

= 9.35 × 10 − 4 M

[ ]

pH = − log H + = − log (9.35 × 10 − 4 ) = 3.03

Equivalence Point: We can also determine the pH at the equivalence point. At the moment when titration is completed, equivalent quantities of the CH3COOH and NaOH solution will be present. Hence, the titrating flask will have a salt solution formed by a weak acid and a strong base. For the solution of such salt (see marginal remark): [H+] =

Ka

i.e. [H + ] =

[ H + ] [A − ] [ HA]

where cacid is the concentration of acidic acid.

...(i)

Ka

Ka =

Kw Ka csalt

The salt concentration in comparison with 0.05 M will halved; Ka K

w

/c

salt

csalt = 0.025 M

[H ] = +

1.0 × 10 −14 ×1.75 × 10 −5 0.025

= 2.65 × 10 −9

pH = – log [H+] = – log 2.65 × 10-9 = ≈ 8.58

Intermediate Points: After determining the starting and end points of the titration, we will now consider pH calculations for the intermediate points. These points of the curve correspond to the simultaneous presence in the solution of an un-titrated weak acid and a salt which is formed as a result of its partial neutralization. Hence, for calculation, we may use the formulas for finding the values of [H+] and pH in

68

Potentiometry-II (pH Metry)

solutions of a weak acid in the presence of its salt of strong base (see marginal remark): [H+] =

K a c acid c salt

Let us calculate the first intermediate point which corresponds to 5 cm3 of 0.05 M NaOH solution poured in. We first determine the quantity (in cm3 of 0.05 M solution) of the residual acid. It will be 25 – 5 = 20 cm3, since 5 cm3 of 0.05 M NaOH solution have titrated CH3COOH. Consequently, cacid in the titration flask is not 0.05M, but cacid =

0.05 × 20 = 0.033 M 30

Let us now determine the concentration of the salt formed at this moment of titration. As we have seen earlier, 5 cm3 of 0.05 M CH3COONa solution were formed, but this quantity of the salt is also in the total volume of 30 cm3 . Therefore, csalt =

0.05 × 5 = 0.008 M 30

A weak acid in the presence of its salt of strong base be be represented as H+ + A −

HA + H2O

−

OH +HA A − + H2O Since for weak acid,

Ka =

[H + ] [A − ] [ HA ] [ H + ] [c

≈

salt ] [c acid ]

For acetic acid Ka is 1.75 × 10-5 Substituting all these data in the formula for finding the pH of the solution, we obtain the following for the first intermediate point: [H + ] =

1.75 × 10 -5 × 0.033 M 0.008

pH = - log [H + ] = - log 7.22 ×10-5 = 4.14 Let us calculate the next point of the titration curve for the moment at which 12.5 cm3 of NaOH solution will be poured in: cacid =

0.05 × (25 − 12.5) = 0.017 M 25 + 12.5

csalt =

0.05 × 12.5 1.75 × 10 -5 × 0.017 M = 0.017 M; [H + ] = 37.5 0.017

pH = –log [H+] = – log 1.75 × 10-5 = 4.76 That is pH = pKa We now calculate the pH of the third intermediate point for V = 15 cm3 cacid =

0.05 × ( 25 − 15) = 0.014 M ( 25 + 15)

csalt =

0.05 × 15 0.021 M 35

[H + ] =

1.75 × 10 -5 × 0.014 0.021

pH = – log [H+] = – log 11.67 × 10–6 = 5.9

After equivalence point (on addition of 25.01 NaOH): In this situation both the excess NaOH and acetate are source of hydroxide ion. We may consider that the contribution from the acetate ion will be small, because the excess of strong base repress the reaction of acetate with water. We have then

69

Electroanalytical Methods -I

[OH − ] ≈ cNaOH =

0.05 (25.01 − 25 ) = 9.99 × 10 6 25.01 + 25

pH = 14.00 – [ – log ( 9.99 × 10 −6 ) = 8.99 On further titration, the pH of the solution will be determined only by excess 0.05 M NaOH solution. Thus, the curve of titration of a weak acid with a strong alkali has the following signs: 1.

The starting point of titration is in a medium which is less acidic than when a strong acid is being titrated,

2.

the equivalence point is in a weakly alkaline medium,

3.

the middle part of the titration curve is more slanting than that of the titration curve of a strong acid;

4.

the titration jump is not great, ranging from pH 8 to pH 10, and accordingly, the vertical part of the curve is considerably smaller than that when a strong acid is being titrated.

Buffering action of the CH3COO − ion: One will see without any difficulty that this curve is much smoother than the curve of titration of a strong acid with a strong alkali, and it does not have a sharp inflection. When HCl solution was titrated with alkali, 22 cm3 of the titrant had to be added in order to change pH by unit, while in this case, approximately 5 cm3 were enough (Fig. 3.7). This difference is due to the fact that when titrating a strong acid with a strong alkali, the concentration of H+ ions decrease only as a result of their combination with OH − ions.

(a)

(b)

Fig. 3.7: pH titration curves: (a) For 0.50 HCl with 0.50 NaOH; (b) 0.50 Acetic acid with 0.50 NaOH.

When titrating a weak acid with a strong alkali, H+ ions combine not only with OH − ions, but also with anions (in this case, with CH3COO − ions), as a result of which [H+] decreases much more rapidly at the beginning of titration, and the titration curve bends downwards much more sharply. Such an effect of the CH3COO − ion, which smoothens out the titration curve, is known as the buffering action. The value of [H+] in the solution of a weak acid in the presence of its salt is determined by the following formula.

70

+

[H ] =

K a c acid

Potentiometry-II (pH Metry)

c salt

It follows that if the acid concentration in the solution is equal to the salt concentration then

K a c acid c salt

= [H + ] = K acid and pH = pK acid

This means that if cacid and csalt have close values in such a mixture, the pH of the solution will remain constant even when considerable quantities of acid and alkali are added. Precisely such a relationship between cacid and csalt is observed in the case of titration of a weak acid with a strong base at the second intermediate point.

SAQ 4 Calculate the pH during the titration of 50.00 cm3 of 0.05 M HCl with 0.10 M NaOH at different stages of titration (i) initial point, (ii) after addition of 10 cm3 of NaOH, (iii) after addition 25 cm3 of NaOH and (iv) after addition of 25.50 cm3 of NaOH. …………………………………………………………………………………………... …………………………………………………………………………………………... .........................................................................................................................................

3.7

MODIFIED GLASS AND SOLID STATE MEMBRANE ELECTRODES

Glass electrode can be made selective for ions other than hydrogen ion by some modifications. This modification is possible by changing the composition of the glass and the internal solution of glass electrode. By adding aluminum oxide to sodium oxide and silicon oxide glass and changing internal filling solution from hydrochloric acid to sodium chloride, such electrode becomes selective to Na+ ions. There is another types of glass electrode with composition of Li2O, Al2O3 and SiO2 is also used as sodium electrode. Sodium electrode has many applications in measurement of sodium in water analysis and in biological fluid analysis. For measuring potassium and ammonium ions, modified glass containing 27 % of Na2O, 4 % Al2O3 and 69 % SiO2. Potassium/ammonium electrode is now replaced by other ion selective electrodes using more selective membrane. Solid State Membrane Electrodes

In solid state membrane electrode we use a doped single crystal membrane in place of glass membrane. These changes enable us to design electrodes which have a response to a number of different anions and cations such as F − , Cl − , and Ag + . A typical design is shown in Fig. 3.8. In this electrode system similar to glass electrode internal solution and electrode form the internal reference. For example, fluoride ion selective electrode consists of LaF3 membrane and an internal Ag, AgCl reference electrode immersed in an internal solution of KF, KCl. LaF3 membrane is highly selective and responds to fluoride ion only. If this electrode used with reference saturated calomel electrode, the complete cell may be written as: Hg,Hg2Cl2 (s)│KCl ║ F − (unknown)│LaF3(s) │NaF(0.1 M) │NaCl (0.1M)│AgCl (s), Ag

71

Electroanalytical Methods -I

Fig. 3.8: A typical solid state electrode

The potential of cell is given by

Ecell = ESCE – ( 0.0591log a Ecell = E * – 0.0591log a

F−

+ E AgCl + E asy + E j )

F−

where E * includes EAgCl ,ESCE, Easy and Ej constant potential representing internal reference electrode, external reference electrode, asymmetry potential, and liquid junction, respectively. Calibration with the known fluoride activity eliminates the need of knowing these constants. Fluoride electrode has many applications such as fluoride determination in bone, air and stack gas samples, chromium plating baths, minerals, water, and toothpastes. Similar to fluoride ion selective electrode many other solid state membrane electrodes can be developed. In Table 3.1, we are listing few such ion selective electrodes. Table 3.1: Some example of solid state membrane ion selective electrodes Selective ion

Membrane

F−

LaF 3

Lower limit of measurement/mol dm-3 10 − 7

Cl −

AgCl

10 − 5

−

AgBr

10

−6

AgI

10

−8

S2 −

Ag2S

10 − 7

SCN −

AgSCN

10 − 6

Ag+

Ag2S

10 − 8

Hg2+

HgS/Ag2S

10 − 8

Cu2+

CuS/Ag2S

10 − 9

Cd2+

CdS/Ag2S

10 − 7

Pb2+

PbS/Ag2S

10

Bi3+

Bi2S3/Ag2S

10 − 11

Br I

72

−

−7

Based on the principle of ion selective electrodes many gas sensing electrodes have been developed in past few years. They are available primarily for the measurement of ammonia, carbon dioxide, and nitrogen oxide. This type of electrode has a gas permeable membrane and an internal buffer solution. The pH of the buffer solution changes as the gas reacts with it. The change is detected by a combination pH sensor within the housing. This type of electrode does not require an external reference electrode. In Table 3.2, we have summarized some commercial gas sensing electrodes.

Potentiometry-II (pH Metry)

Table 3.2: Several typical gas sensing electrodes Test ion

Internal electrolyte NH4Cl

Internal ion selective electrode (ISE) pH

NH3

Membrane

ptfe (polytetrafluoroethylene)

CO2

NaHCO3

pH

ptfe

NOx

NaNO2

pH

ptfe

SO2

K2S2O5

pH

silicone rubber

H2S

Citrate buffer

S2-

silicone rubber

Applications Ion Selective Electrodes

Ion selective electrodes along with pH-sensitive glass electrode are widely used in clinical, biological, water, air, oceanographic, and pharmaceutical research and routine analytical determinations. So far there are reliable commercially available electrodes for detecting H+, F–, Cl–, Br–, I–, Cd2+, Cu2+, CN–, BF −4 , Pb2+, NO 3− , ClO −4 , Ag+, S2–, Na+, K+, and SCN–, for NH3, H2S, SO2, CO2, nitrogen oxides gases, and for several different enzymes. Glass membrane electrode is the most commonly used ion selective electrode. pH measurements have many applications some of which are summarized below: •

pH metric or electrometric methods help in detecting the end point of acid-base titration more accurately and precisely as compared to indicator methods.

•

pH metry is an important analytical tool in studying the acid-base equilibria which is controlled by the carbon dioxide-bicarbonate-carbonate equilibrium system in most natural waters.

•

The estimation of alkalinity and acidity based on pH metry serves a useful information of buffering capacity of water.

•

In water and wastewater treatment, it gives an estimate of available of alkalinity to react with the coagulant viz alum, Ferrous sulphate etc. or otherwise to be supplemented with lime.

•

Industrial process control especially in batch or flow-through configurations; through online pH monitoring and chemical dosing system.

•

In neutralization of wastewaters, to evaluate the doses of acid or alkali to be added.

•

Development of biosensors based pH sensitive immobilized enzymes and other academic studies.

Further the flexibility in available configurations allows the ions mentioned above to be monitored in a single sample solution (batch mode) or continuously in a flow through apparatus (flow-injection analysis).

73

Electroanalytical Methods -I

3.8

SUMMARY

One of the most common and earliest applications of potentiometry is pH determination, and titration for the determination of electro active species. Through development of electrodes that selectively determine target ions, potentiometry in general is replacing many older, more expensive and time consuming techniques for analytically monitoring and measuring ion activity. Recent developments in the ion selective electrodes (ISE) branch of potentiometry have made the monitoring of inorganic, organic, gaseous and biologically important ions possible. The flexibility in available configurations allows these ions to be monitored in a single sample solution (batch mode) or continuously in a flow through apparatus (flow-injection analysis).

3.9

TERMINAL QUESTIONS

1.

Discuss the source of pH dependence in a glass membrane electrode.

2.

What is the source of the asymmetry potential in a glass membrane electrode?

3.

What are the advantages of a pH metric titration over a direct pH metry?

4.

Drive an expression for the ‘operational definition of pH’.

5.

What is the source of the potential of an ion selective electrode used to determine the concentration of fluoride ion?

6.

Calculate the pH during the titration of 50.00 cm3 M NaOH with 0.10 M HCl after the addition of the following volume of acid : (i) 24.50 cm3, (ii) 25.00 cm3 and (iii) 25.50 cm3.

7.

Calculate the pH during titration of 50.00 cm3 M NaCN with 0.10 M HCl after the addition of the following volume of acid : (i) 0.00 cm3, (ii) 10 cm3, (iii) 25.00 cm3 and (iv) 26 cm3. (Hint: Kw = KaKb and acid dissociation constant for HCN = 6.2 × 10 −10 )

3.10 ANSWERS Self Assessment Questions

74

1.

It is not possible to determine the values of asymmetry potential as well as liquid- junction potential in glass/calomel electrode, therefore, it is necessary to calibrate glass membrane electrode with suitable buffer solutions before use.

2.

When glass electrode is placed in a test solution its glass membrane will have an inner and outer hydrated layer and potential difference is developed due to the difference in hydrogen ion activities between test solution and outer hydrated surface of glass electrode as well as inner solution as inner hydrated surface. This potential is called boundary potential and it varies with the activity or pH of the solution. Overall boundary potential is the potential difference between both the boundary potentials.

3.

i)

Alkaline error

ii)

Acid error

iii)

Variation in junction potential

iv)

Error in the pH of the standard buffer

v)

Temperature

4.

vi)

Calibration procedures

vii)

Equipment related

Potentiometry-II (pH Metry)

Initial Point Before any base is added, the solution is 0.05 M in H+, and pH= – log[H+] = – log 0.0500 = 1.30

After Addition of 10.00 M of acid: The hydrogen ion concentration is decreased as a result of the reaction with the base and dilution. So the analytical concentration of HCl is cacid =

No. mmol HCl remaining after addition of NaOH Total volume solution

=

=

Original no. mmol HCl − No. mmol NaOH added Total volume solution (50.00 cm 3 × 0.05 M ) − (10.00 cm 3 × 0.10 M ) 50.00 cm 3 + 10.00 cm 3 .

= 2.500 × 10 −2 M [H + ] = 2.500 × 10 − 2 M and pH = − log [ H + ] = − log (2.500 × 10 − 2 ) = 1.60

After addition of 25.00 M of acid: The Equivalence Point At the equivalence point, neither HCl nor NaOH is in excess and so the concentrations of hydrogen and hydroxide ions must be equal. Substance equality into the ion-product constant for water yields

[H + ] =

K w = 1.00 ×10 −14 = 1.00 × 10 −7 M

pH = − log (1.00 × 10 −7 ) = 7.00

After Addition of 25.10 M of acid: The solution now contains an excess of NaOH, and we can write c base = =

No.mmol NaOH added − Original no mmol HCl Total volume solution

25.10 × 0.10 − 50.00 × 0.05 = 1.33 × 10 − 4 M 75.10

and the equilibrium concentration of hydroxide ion is

[OH − ] = c base = 1.33 × 10 −4 M pOH = − log (1.33 × 10 − 4 ) = 3.88 and pH = 14.00 − 3.88 = 10.12

Terminal Questions 1.

When glass electrode is placed in a test solution its glass membrane will have an inner and outer hydrated layers and potential difference is developed due to the difference in hydrogen ion activities between test solution and outer hydrated surface of glass electrode as well as inner solution and inner hydrated surface.

75

Electroanalytical Methods -I

This potential is called boundary potential and it varies with the activity or pH of the solution. Overall boundary potential is the potential difference between both the boundary potentials. Concentration of inner solution is kept constant, thus the boundary potential is a measurement of the hydrogen ion activity or the pH of the external solution. 2.

The asymmetry potential in a membrane arises from difference in the structure of the inner and outer surfaces. These difference may be due to the manufacture reason or due to its use.

3.

pH titrations generally offer increased accuracy and precision. Accuracy is increased because measured pH are used to detect rapid changes in activity that occur at equivalence point of the titration. Furthermore, it is the change in pH versus titre volume rather than absolute value of pH that is of interest. Thus, the errors due to liquid-junction potentials and activity coefficients are minimized.

4.

Cell potential for the standard buffer can be expressed as (Ecell )s = E* – 0.0592 (pH)s

… (i)

Cell potential for unknown solution will be expressed as (Ecell )u = E* – 0.0592 (pH)u

…(ii)

To eliminate E* subtract Eq. (i) from Eq. (ii), we find (pH)u = (pH)s –

( E cell ) u − ( E cell ) s 0.0591

… (iii)

Eq. (iii) is the operational definition of pH. 5.

When ion selective electrode is dipped in the solution containing fluoride ions, the equilibrium will be established between both the fluoride ions in test solution and LaF3 crystal and fluoride ions in inner solution and LaF3. The activity of the F– at the inner surface is likely to be different to that at the outer surface. This results in a development of the diffusion potential between two surfaces similar to liquid junction potential. As the activity of internal solution is constant value, the diffusion potential is, thus, dependent on the activity of F– in the test solution.

6.

i)

At 24.50 cm3 added, [H+] is very small and cannot be computed from stoichiometric considerations but can be obtained from [OH − ] [OH − ] = c base =

=

Original no. mmol NaoH − No. mmol HCl added Total volume of solution

50.00 × 0.05 − 24.50 × 0.10 = 6.71× 10 − 4 M 50.00 + 24.50

[H + ] = K w / (6.71× 10 −4 ) = 1.00 × 10 −14 /(6.71× 10 −4 ) = 1.49 × 10 −11 M pH = − log(1.49 × 10 −11 ) = 10.83

ii)

76

This is the equivalence point where [H+]= [OH-]

+

[H ] =

Kw =

1.00 × 10

−14

= 1.00 ×10

−7

M

Potentiometry-II (pH Metry)

pH = − log (1.00 × 10 −7 ) = 7.00

iii)

At 25.50 cm3 added, [H + ] = c HCl =

( 25.50 × 0.10 − 50.00 × 0.05) 75.50

= 6.62 × 10 −4 M

= − log (6.62 × 10 −4 ) = 3.18

pH

7.

i)

The pH of a solution of NaCN can be calculated as CN − + H 2O
HCN + OH −

Kb =

[OH − ][HCN ] [CN − ]

=

K w 1.00 × 10 −14 = = 1.61 × 10 −5 −10 Ka 6.2 × 10

Sinceanequ ivalentamo untof [OH − ] and [ HCN] areformed [OH − ] = [ HCN] [CN − ] = c NaCN − [OH − ] ≈ c NaCN = 0.05M

Substitution into the above dissociation-constant expression gives, after rearrangement, [OH − ] = K b cNaCN =

1.61 × 10−5 × 0.05 = 8.97 × 10− 4

pH = 14.00 − (− log 8.97 × 10 −4 ) = 10.95

ii)

10.00 cm3 of Reagent Addition of acid produces a buffer with a composition given by

50.00 × 0.05 − 10.00 × 0.100 1.50 = M 60.00 60.00 10.00 × 0.10 1.000 = = M 60.00 60.00

c NaCN = c HCN

These values are then substituted into the expression for the acid dissociation constant of HCN to give [H+] directly: [H + ] =

[H + ] =

K a × c acid csalt

6.2 × 10−10 × (1.000 / 60.00) = 4.13 × 10−10 1.50 / 60.00 pH = − log (4.13 × 10−10 ) = 9.38

iii)

25.00 cm3 of Reagent This volume corresponds to the equivalence point, where the principal solution species is the weak acid HCN. Thus,

77

Electroanalytical Methods -I

c HCN =

25.00 × 0.10 = 0.033M 75.00

Applying following Equation gives [H + ] = K a c HCN = 6.2 × 10 −10 × 0.033 = 4.45 × 10 −6 M pH = − log (4.45 × 10 −6 ) = 5.34

iv)

26.00 cm3 of Reagent The excess of strong acid now present represses the dissociation of the HCN to the point where its contribution to the pH is negligible. Thus, [H + ] = c HCl =

26.00 × 0.10 − 50.00 × 0.05 = 1.32 × 10 −3 M 76.00 pH = − log(1.32 × 10 −3 ) = 2.88

78

Potentiometry-II (pH Metry)

Appendix I Standard Electrode Potentials* Reaction

E0 at 25° C,V

MnO 4− + 8 H+ + 2e
Mn2+ + 4H2O

+ 1.51

Cl2(g)+ 2e
2Cl −

+ 1.359

Cr2 O2– + 14 H+ + 6e
2Cr3+

+ 1.33

O2 (g)+4H+ + 4e
2H2O

+ 1.229

Br2(aq) + 2e
2Br −

+ 1.087

Br2(l) +2e
2Br −

+ 1.065

Ag+ + e
Ag (s)

+ 0.799

Fe3+ + e
Fe2+

+ 0.771

I-3 + 2e
3I −

+ 0.536

Cu2+ + 2e
Cu (s)

+ 0.337

UO22+ + 4H++2e
U4+ + 2H2O

+ 0.334

Hg2Cl2 (s) + 2e
2Hg (l) + 2Cl −

+ 0.268

AgCl(s) + e
Ag(s) + Cl −

+ 0.222

Ag(S2O3)3-2 + e
Ag (s) + 2S2O 32 −

+ 0.017

2H+ + 2e
H2(g)

0.000

AgI(s) + e
Ag(s) + I −

– 0.151

PbSO4 + 2e
Pb(s) + SO 24 −

– 0.350

Cd2+ + 2e
Cd (s)

– 0.403

Zn2+ + 2e
Zn(s)

– 0.763

Ce4+ + e
Ce3+

– 1.70 V

Mg 2 + + 2e
Mg (s)

– 2.363

79